Chapter 11, Problem 10QC

To determine

To find: The expanded form of the given binomial.

Answer to Problem 10QC

Theexpanded form is $64a^6+192a^{5}b+240a^4{b}^2+160a^3{b}^3+60a^2{B}^4+12a$ .

Explanation of Solution

Given:

The given binomial is ${\left(2a+b\right)}^6$ .

Calculation:

Consider given binomial is,

  ${\left(2a+b\right)}^6$

Then, the expanded form is,

  $\begin{array}{c}{\left(2a+b\right)}^6= {\left(2a\right)}^6+6{\left(2a\right)}^{5}b+15{\left(2a\right)}^4{b}^2+20{\left(2a\right)}^3{b}^3+15{\left(2a\right)}^2{B}^4 +6\left(2a\right)b^5 +b^6\\ =64a^6+192a^{5}b+240a^4{b}^2+160a^3{b}^3+60a^2{B}^4+12a\end{array}$